Author(s)

Jin Chen

Corresponding Author

Jin Chen

Abstract

When studying a continuous model theorem in functional analysis, we come across an indirect proof method. For example, the proof of compactness theorem is extremely abstract and complicated. An indirect proof method is given for a continuous mode theorem in nonlinear functional analysis. Weakly consistent continuous and consistently continuous definitions make it easier for you to compare and better analyze consistent and continuous definitions. In the functional analysis, there are metric spaces, linear normed spaces and inner product spaces. The following is a brief description of the consistent continuity in the metric space. In the functional analysis, there are also concepts such as strong convergence, weak convergence, and weak convergence of functional sequences. On the basis of topological sequence, this paper solves the critical path by calculating the earliest occurrence time of each vertex and marking the corresponding path. For example, the proof of compactness theorem is extremely abstract and complex. Because functional analysis is a generalization of mathematical analysis, the definition of uniform continuity in mathematical analysis is extended to linear normed spaces.

Keywords

Uniformly continuous, identical continuous, sequentially convergent